System and method for estimating the multi-path delays in a signal using a spatially blind antenna array

ABSTRACT

A method is described that enables a system to estimate the individual times of arrival of multi-path signals components in a received signal while blind to the particular angular response characteristics of an antenna array. Additionally, a system is described that estimate the impulse response of the modulation channel. The impulse response is used to generate impulse response estimates for all multi-path signal components without reference to the actual angle of arrival of the signal. The impulse response for the multi-path constituents are directly associated with the time delays on each path, providing delay estimates for each path.

CROSS REFERENCES

The present application is co-pending with and claims priority benefitof U.S. provisional application entitled “Geolocation of MobileAppliances” Ser. No. 60/418,342 and filed on Oct. 16, 2002, the entiretyof which is incorporated herein by reference.

The present application is related to and concurrently filed withapplications titled “A NETWORK OVERLAY GEO-LOCATION SYSTEM WITH SMARTANTENNAS AND METHOD OF OPERATION” Ser. No. ______, “WIRELESSCOMMUNICATION NETWORK MEASUREMENT DATA COLLECTION USING INFRASTRUCTUREOVERLAY-BASED HANDSET LOCATION SYSTEMS” Ser. No. ______, “NETWORKOVERLAY LOCATION SYSTEM AND METHOD FOR AIR INTERFACE WITH FREQUENCYHOPPING” Ser. No. ______, “A SYSTEM AND METHOD FOR ENHANCING THEACCURACY OF A LOCATION ESTIMATE”, Ser. No. ______, and “SYSTEM ANDMETHOD FOR OPERATING A NETWORK OVERLAY GEO-LOCATION SYSTEM WITHREPEATERS” Ser. No. ______, filed Oct. 16, 2003, the entirety of each ofthese applications is incorporated herein by reference.

BACKGROUND

Digital signals are often filtered using a pulse shaping filter prior totransmission. This is typically done to contain the signal bandwidth andminimize intersymbol interference between signal componentscorresponding to different digital symbols. This is shown in FIG. 1,where symbols from a digital constellation corresponding to theinformation being modulated are passed though a pulse shaping filter. InFIG. 1, the digital data to be transmitted is mapped into a complexsignal constellation in block 101. For example, the complex signalconstellation used may be an M-ary QAM constellation; however otherconstellations are also used. The mapped constellation undergoes pulseshaping in a filter as shown in block 102. Several methods known in theart can be employed for pulse shaping. The filtered constellation signalis converted to a radio frequency, represented as block 103, fortransmission over the ether.

An artifact of this signal generation provides an unintended featurethat has been the focus of recent investigation. If the digital signalis passed through a multi-path channel, the channel output is anaggregate of delayed, possibly faded and phase shifted replicas of theoriginal digital signal. In practice, this occurs if a multiplicity ofreflections of the transmitted signal are contained in the receivedsignal. The delays can either be absolute, if the time of arrival of thedirect path signal is known, or could be relative delays between themulti-path components. If these multi-path signals are received at theantenna array, the received signal can be mathematically formulated as aspace-time signal.

When the characteristics of the pulse shaping filter and the antennaarray are known, a theory of signal processing can be applied toestimate the multi-path delays of the signal components and theirparticular directions of arrival. This signal processing analysis isreferred to as space-time processing. Space-time processing is a groupof techniques that may be applied to resolve the received space-timesignals into a sum of faded space-time signals. Each of these space timesignals corresponds to the particular angle of arrival and time delay ofone of the original multi-path signal components.

It is advantageous to develop a mathematical description of the priorart technique to convey the manner in which multi-path delays and angleof arrival (“AOA”) are currently calculated to fully appreciate thedistinctness of the to be disclosed subject matter. The prior art methodis illustrated in FIG. 2.

A column vector r_(k) denotes the received signal at antenna k of anantenna array with m antennas, where k=1,2, . . . m. An impulse responseh_(k) of the multi-path channel is derived from r_(k), represented inblock 201. The derivation of the column vector h_(k) can be achieved byvarious methods and implemented with signal processors through softwareand/or hardware.

If the source data associated with this received block is known, asimple means of extracting h_(k) is via the delay matrix correspondingto this source data. The delay matrix Z is formed by stacking symbolshifted copies of the source data in rows to a depth that defines theextent of the desired impulse response and truncating its longerdimension to match the length of r_(k). An estimate of h_(k) is givenby: h_(k)=(ZZ^(H))⁻¹Zr_(k).

Alternate means for estimating the impulse response may provide betteror worse estimates, depending on the particular modulation format of thedata, the block length, the fading characteristics of the multi-pathchannel and possibly other parameters. Some of these other methods areblind to the actual data transmitted, using properties of either thesignal modulation and/or of the channel instead.

Having estimated the impulse response of the multi-path channel from thesource to antenna k of the array, a vectorized space-time impulseresponse over the entire array is formed, in block 202, by stacking theindividual impulse response estimate h_(k) into a long column vector{right arrow over (I)}, given by:$\overset{\rightarrow}{I} = {\begin{bmatrix}h_{1} \\\ldots \\h_{k} \\\ldots \\h_{m}\end{bmatrix}.}$

Theoretically, {right arrow over (I)} can be expressed as${I = {{\sum\limits_{i = 1}^{n}I_{i}} + N}},$where {right arrow over (I)} indexes the individual space-time impulseresponses, i=1,2, . . . , n, of the distinct multi-path components and Nis a noise vector.

Any particular I_(i) is of the form I_(i)=β_(i)ηa(θ_(i)){circle around(×)}g(τ_(i)) in which β_(i) denotes the fade multiplier for the signalblock, and η denotes the signal amplitude at the transmitter. a(θ_(i))denotes the antenna response corresponding to a signal arriving fromangle θ_(i), {circle around (×)} denotes the Khatri-Rao product, andg(τ_(i)) denotes the pulse shaping waveform delayed by τ_(i) andsampled. This formation of an outer product and aggregate in thecovariance matrix, is represented in block 203. The formation of thecovariance matrix can be implemented with signal processors or othercomputer processors through software and/or hardware devices.

The vectors a and g can be expressed as:${{a\left( \theta_{i} \right)} = \begin{bmatrix}{a_{1}\left( \theta_{i} \right)} \\{a_{2}\left( \theta_{i} \right)} \\\ldots \\{a_{m}\left( \theta_{i} \right)}\end{bmatrix}},{and}$ ${g\left( \tau_{i} \right)} = {\begin{bmatrix}{g\left( {{{- l}\quad T_{s}} - \tau_{i}} \right)} \\{g\left( {{{- \left( {l - 1} \right)}T_{s}} - \tau_{i}} \right)} \\\ldots \\{g\left( {{l\quad T_{s}} - \tau_{i}} \right)}\end{bmatrix}.}$

In the equation for g(τ_(i)), l denotes the sampling depth of the pulseshaping function and T_(s) is the sampling time.

Given this formation of the space-time impulse response, when the numberof multi-path components is smaller than the dimension of the symbolsampled impulse response vector I, it is possible to estimate themulti-path delays τ_(i) and the multi-path arrival angles θ_(i).

The prior art approach to estimating the delays and arrival anglesrelies on an explicit knowledge of the aggregate of all vectors:${a\left( \theta_{i} \right)} = \begin{bmatrix}{a_{1}\left( \theta_{i} \right)} \\{a_{2}\left( \theta_{i} \right)} \\\ldots \\{a_{m}\left( \theta_{i} \right)}\end{bmatrix}$for all angles θ_(i). This aggregate is termed the array manifold, A. Itis assumed that the pulse shaping function at the transmitter is knownat the receiver. Denoting the aggregate of all vectors as${g\left( \tau_{i} \right)} = \begin{bmatrix}{g\left( {{{- l}\quad T_{s}} - \tau_{i}} \right)} \\{g\left( {{{- \left( {l - 1} \right)}T_{s}} - \tau_{i}} \right)} \\\ldots \\{g\left( {{l\quad T_{s}} - \tau_{i}} \right)}\end{bmatrix}$for all values of τ_(i) as the delay manifold, ç, then the quantityK=A{circle around (×)}ç represents the space-time manifold.

The observation that I_(i) is contained in K leads to a primaryobjective of space-time processing: searching the manifold K forweighted linear combinations of vectors I_(i) such that a best fit tothe observed space-time impulse response {right arrow over (I)} isgenerated as shown in block 204. A variety of techniques may be appliedfor this purpose, such as Multiple Signal Classification (MUSIC), TheMethod of Alternating Projections (APM), etc, which can be implementedthrough software and/or hardware. Other mathematical descriptions forjointly estimating the angle of arrival (“AOA”) and time delays can befound in Ziskind, I., Wax, M., “Maximum likelihood localization ofmultiple sources by alternating projection”, IEEE Trans. Acoust.,Speech, Signal Process. vol. 36, no. 2 (October 1988), 1553-1560; VanDer Veen, M, Papadias, C. B., Pautraj, A. J., “Joint angle and delayestimation” IEEE Communications Letters vol. 1-1 (January 1997), 12-14;Schmidt, R. O. “Multiple emitter location and signal parameterestimation” Proc. RADC Spectrum Estimation Workshop, (March 1999),243-258; Young-Fang Chen, Michael D. Zoltowski “Joint Angle and Delayestimation of DS-CDMA communication systems with Application to ReducedDimension Space-time 2D Rake Receivers”, IEEE Transactions on SignalProcessing; Paulraj, A. J., Papadias, C. B., “Space-Time SignalProcessingfor Wireless Communications”, IEEE Signal Processing Magazine,vol. 11 (November 1997), 49-83; Paulraj, A. J., Papadias, C. B.,“Space-Time Signal Processingfor Wireless Communications: A Survey”Information System Laboratory, Stanford University; and Haardt, Brunnerand Nossek “Joint Estimation of 2-D Arrival Angles, Propagation Delays,and Doppler Frequencies in Wireless Communications”; all of which areincorporated herein by reference.

An object of the disclosed subject matter is to obviate the deficienciesof the prior art by removing the dependency of the time delay estimatesfrom the spatial and gain characteristics of an antenna array thusallowing multi-path delay estimates to be obtained for any genericantenna array. This object is achieved by recasting the array manifoldin a spatially blind manner so as to be independent of the arraycharacteristics.

It is another object of the disclosed subject matter to present animproved method for estimating the multi-path delays in a signalreceived at any k array element. The method includes estimating animpulse response at each k antenna, generating a space-time impulseresponse, and forming a covariance matrix and resolving the covariancematrix with a known antenna array manifold. Additionally, a novelimprovement to known methods includes the step of resolving thecovariance matrix with a fictitious antenna array manifold.

It is still another object of the disclosed subject matter to present anovel method for estimating the multi-path delays in a signal using aspatially blind antenna array. The method includes generating an impulseresponse h_(k) for each antenna k in the antenna array and determining avectorized space-time impulse response I over the antenna array. Themethod further includes creating a covariance matrix C, a fictitiousmanifold A_(f), where A_(f) is spatially blind and independent of thearray characteristics, and then resolving the covariance matrix C withthe fictitious manifold A_(f) to estimate the multi-path delays τ_(i) ina manner independent of the array characteristics.

It is yet another object of the disclosed subject matter to present amethod of estimating the multi-path delays of a sequence of j blocks ofa signal received at an antenna array comprising k antenna elementsindependently of the spatial array characteristics of the antenna array.The method includes deriving a channel impulse response estimatesh_(j,k) for each block j at each antenna k and determining a vectorizedaggregate space-time impulse response I for each block j. The methodincludes the steps of forming an estimated covariance matrix for thesequence of j blocks, forming an array manifold A_(f) void of spatialinformation; and then resolving the covariance matrix with thefictitious array manifold A_(f) to determine the multi-path delaysτ_(i).

It is also an object of the disclosed subject matter to present a novelsystem for estimating the multi-path delays in a signal using aspatially blind antenna array. The system includes an antenna array, ameans for generating an impulse response h_(k), a means determining avectorized space-time impulse response I and a means for creating acovariance matrix C. The system also includes a means for creating afictitious manifold A_(f), wherein A_(f) is spatially blind andindependent of the array characteristics; and a means for resolving thecovariance matrix C with the fictitious manifold A_(f) to estimate themulti-path delays τ_(i) independent of the array characteristics.

These objects and other advantages of the disclosed subject matter willbe readily apparent to one skilled in the art to which the disclosurepertains from a perusal or the claims, the appended drawings, and thefollowing detailed description of the preferred embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a representative flow chart of a portion of a prior art systemand/or method for transmitting a digital signal.

FIG. 2 is a representative flow chart of a prior art receiving systemand/or method for space-time processing a received signal.

FIG. 3 is a representative flow chart for spatially blind space-timeprocessing a received signal according to a system/method of the presentdisclosure.

FIG. 4 is a representative flow chart for estimating delays of multipathcomponents of a received signal according to an embodiment of asystem/method of the present disclosure

DETAILED DESCRIPTION

The present disclosure presents a system and method for a technique fordetermining the individual times of arrival of multipath signalcomponents in a received signal. The delays in the multipath componentsare determined by creating a fictitious array manifold A_(f) in whichthe directional knowledge of the array is absent. As discussed earlier,the vector a is produced with the knowledge of all the vectors for allangles θ_(i), is represented as:${a\left( \theta_{i} \right)} = {\begin{bmatrix}{a_{1}\left( \theta_{i} \right)} \\{a_{2}\left( \theta_{i} \right)} \\\ldots \\{a_{m}\left( \theta_{i} \right)}\end{bmatrix}.}$

To remove the dependence on θ_(i), each dimension of the array takes allpossible complex numbered values. The independent aggregate vector isthen given by: ${{a\left( \theta_{i} \right)} = \begin{bmatrix}a_{1} \\a_{2} \\\ldots \\a_{m}\end{bmatrix}},$where each a_(k) is contained in the complex number space C, so that thefictitious array manifold A_(f) is the space C^(m). This formulationallows space-time processing to proceed blind to the specificcharacteristics of the antenna array such as element spacing, elementgain, etc.

As discussed above, the signal processing flow for the established priorart technique is shown in FIG. 2. This technique requires knowledge ofthe antenna array manifold A, i.e., one must have explicit knowledge ofthe antenna response corresponding to a signal arriving at each possibleangle for each element in the antenna array. As discussed earlier, it isnot always possible to easily obtain the antenna array manifold A ascalibration of the antenna array is a tedious, time-consuming, andexpensive task. The prior art technique allows for determination of anestimation of multipath delays and the particular angles of arrival ofthe multipath signals.

The signal processing flow for the above-discussed subject matter, onthe other hand, employs a fictitious array manifold as shown in FIG. 3.An estimate of the impulse response is determined at each antennaelement as shown in block 301. From the impulse response, a space-timeimpulse response is generated in block 302 and an outer product andaggregate in the covariance matrix is formed in block 303 in a mannersimilar to that as discussed for the prior art. In block 304 thecovariance matrix is resolved with the generalized fictitious antennaarray manifold A_(f) defined above rather than the known antenna arraymanifold A as shown in FIG. 2. While the novel techniques describedherein does not allow for resolution of the particular angles of arrivalof the multipath signals, it does allow for determining an estimation ofthe time delays of the multipath components given an antenna array witharbitrary and unknown properties. Therefore, the novel techniques hereindescribed allow for the use of antennas separated by arbitrary distancesand with arbitrary gain characteristics while still obtaining importantinformation: the time delays of multipath signal components.

To facilitate understanding of the novel techniques described herein, anexample follows for the case of a signal received at a two antenna arrayin which the established prior art space-time techniques derive delayestimates on a multi-path signal, followed by estimates developed by useof a spatially blind antenna array according to an embodiment of thepresent disclosure.

A sequence of blocks of signal received concurrent in time at the twoantennas are denoted by r_(jk) where k=1, 2 and j=1,2, . . . J, theindex j counts the blocks and of course the index k references theantennas, two in this case. It is, of course, to be understood by thoseof skill in the art that the present discussion is exemplary only andthat the techniques described herein are in no way limited to antennaarrays composed of only two antenna elements. The disclosed techniquesare applicable to antenna arrays of an arbitrary number of antennaelements. If the source data associated with each block is known,possibly from demodulating the received signal at either or both of theantennas, or by demodulation at some other receiver, the delay matrixcan be developed as illustrated in the previous section and this can beused to derive channel impulse response estimates for each block at eachantenna. Thus h_(j,k)=(Z_(j)Z_(j) ^(H))⁻¹Z_(j)r_(j,k), where h_(jk) isthe impulse response estimate for block j and antenna k, and Z_(j) isthe delay matrix for block j.

The vectorized aggregate space-time impulse response for block j isgiven by ${I_{j} = \begin{bmatrix}h_{j,1} \\h_{j,2}\end{bmatrix}},$from which an estimated covariance matrix for the sequence of blocks canthen be formed as $C = {\sum\limits_{j = 1}^{J}{I_{j}{I_{j}^{H}.}}}$

Most known methods for extracting an arrival angle do so by operationson C. Other methods that operate on the sequence {I_(j)} differently canalso be used.

All established techniques for estimating the path delays and arrivalangles in the space-time context require knowledge of the array manifoldA which is the aggregate of all possible vectors:${a(\theta)} = \begin{bmatrix}{a_{1}(\theta)} \\{a_{2}(\theta)}\end{bmatrix}$in which a_(k)(θ) is the complex gain of antenna k for a signal arrivingfrom angle θ. Explicit knowledge of antenna gain for each antenna isrequired. In addition, the pulse shaping function and thus the delaymanifold ç as detailed in the previous section are also needed.

Most established prior art techniques estimate the delays and arrivalangles of the multi-path signals by decomposition of the covariancematrix into a sum of estimated impulse responses. This is done using thespace-time manifold:K=A{circle around (×)}ç.

The estimated covariance matrix is resolved into estimates of theimpulse responses associated with each multi-path component. Eachestimated impulse response is drawn from K and therefore points directlyto a particular delay and arrival angle.

In accordance with an embodiment of the disclosed subject matter, anexample using a spatially blind estimation techniques for the time delayestimates is illustrated below for the same scenarios as describedabove.

To obtain the delay estimate without knowledge of the antenna array oran explicit knowledge of the antenna gains, a fictitious array manifoldis used, A′_(f), given by the aggregate of all vectors,$a = \begin{bmatrix}a_{1} \\a_{2}\end{bmatrix}$where a₁ and a₂ range over the set of complex numbers. It is worthy tonote that while the delay estimates can be determined for multi-pathsignals independently of the antenna characteristics, angle of arrivalcannot be determined in the same manner. This is not a problem if allthat is of concern is the relative time delays of the multipath signalsand the angles of arrival of those multipath signals is not ofconsequence.

The process estimates the delays without knowledge of the actual arraymanifold A by using instead the fictitious manifold A′_(f), so thatA′_(f) replaces A in the space-time manifold K=A{circle around (×)}ç.This then becomes the aggregate of vectors, ${K = \begin{bmatrix}{a_{1}{g(\tau)}} \\{a_{2}{g(\tau)}}\end{bmatrix}},$as a₁ and a₂ cover the space of complex numbers and τ covers theexpected range of multi-path delays.

The estimated covariance matrix is resolved in order to estimate theimpulse responses associated with each multi-path component. Eachestimated impulse response is drawn from K_(f) and maps directly to aparticular τ and complex vector [a₁, a₂]^(t). The signal processing flowfor this embodiment is shown in FIG. 4. An estimate of the impulseresponse is determined at each antenna element as shown in block 401.From the impulse response, a space-time impulse response in generated inblock 402 and an outer product and aggregate in the covariance matrix isformed in block 403. In block 404, the covariance matrix is resolvedwith the specific fictitious antenna array manifold A′_(f).

The earliest arrival time is of particular interest in many applicationssuch as cellular geo-location. This technique, termed BLind Space Time(“BLST”) permits the estimation of relative delays in multi-path signalcomponents using arbitrary configurations of antennas in an array. This,for example, allows one to apply the method to antennas that areseparated by arbitrary distances and with arbitrary gaincharacteristics. Existing antenna configurations in the cellularwireless network can be used without the need for calibration of thearray. Calibration is a tedious task that needs to be updated often as aknown array is required for signal processing according to the priorart. Thus the use of Blind-Space Time for estimating multi-path delaysallows for the application to any arbitrary antenna array withoutrequiring calibration.

While preferred embodiments of the present inventive system and methodhave been described, it is to be understood that the embodimentsdescribed are illustrative only and that the scope of the embodiments ofthe present inventive system and method is to be defined solely by theappended claims when accorded a full range of equivalence, manyvariations and modifications naturally occurring to those of skill inthe art from a perusal hereof.

1. In a method for estimating the multi-path delays in a signal received at an antenna array of k antenna elements, comprising estimating an impulse response at each k antenna, generating a space-time impulse response, forming a covariance matrix and resolving the covariance matrix with a known antenna array manifold, the improvement comprising the step of resolving the covariance matrix with a fictitious antenna array manifold.
 2. A method for estimating the multi-path delays τ_(i) in a signal using a spatially blind antenna array comprising k arbitrary antenna elements, comprising the steps of: generating an impulse response h_(k) for each antenna element k in the antenna array; determining a vectorized space-time impulse response I over the antenna array; creating a covariance matrix C; creating a fictitious array manifold A_(f), wherein A_(f) is spatially blind and independent of the array characteristics; and resolving the covariance matrix C with the fictitious manifold A_(f) to thereby estimate the multi-path delays τ_(i) independent of the array characteristics.
 3. The method of claim 2 wherein the impulse response estimate h_(k) is determined from the equation: h _(k)=(ZZ^(H))⁻¹ Zr _(k) where Z is a delay matrix and r_(k) is the column vector of the received signal at antenna element k of the antenna array, where k=1,2, . . . m.
 4. The method of claim 3 wherein the space-time impulse response vector I is formed by stacking the individual impulse response estimates h_(k) into a column vector.
 5. The method of claim 2 wherein the fictitious manifold A_(f) is the aggregate of all vectors: ${a = \begin{bmatrix} a_{1} \\ a_{2} \\ \vdots \\ a_{m} \end{bmatrix}},$ where a_(k)(k=1,2, . . . m) range over the set of complex numbers, where m is the number of antenna elements in the array.
 6. The method of claim 2 wherein the covariance matrix C is generated according to the following equation: C = ∑I  I^(H).
 7. The method of claim 2, wherein the fictitious array manifold A_(f) is used to form the space-time manifold and the space-time manifold operates to resolve the multi-path delays
 8. The method of claim 2 wherein the step of resolving the covariance matrix C to determine multi-path delays τ_(i) uses the method of MUltiple SIgnal Classification (MUSIC) techniques.
 9. The method of claim 2 wherein the step of resolving the covariance matrix C to determine multi-path delays τ_(i) uses the Method of Alternating Projection (APM).
 10. A method of estimating the multi-path delays τ_(i) of a sequence of j blocks of a signal received at an antenna array of k isotropic antenna elements, independently of the spatial array characteristics of the antenna array, comprising the steps of: deriving channel impulse response estimates h_(j,k) for each block j at each antenna k; determining a vectorized aggregate space-time impulse response I for each block j; forming an estimated covariance matrix for the sequence of j blocks; providing an array manifold A_(f) void of spatial information; and, resolving the covariance matrix with the array manifold A_(f) to determine the multi-path delays τ_(i).
 11. The method of 10, wherein the impulse response estimate h_(j,k) for block j is determined from the equation: h _(j,k)=(Z _(j) Z _(j) ^(H))⁻¹ Z _(j) r _(j,k) where Z_(j) is a delay matrix for block j and r_(jk) is the column vector of the received signal for block j at antenna k of the antenna array, where k=1,2, . . . m.
 12. The method of 11, wherein the space-time impulse response vector I is formed by stacking the individual impulse response estimates h_(jk) into a column vector.
 13. The method of 10, wherein the fictitious manifold A_(f) is the aggregate of all vectors: ${a = \begin{bmatrix} a_{1} \\ a_{2} \\ \vdots \\ a_{m} \end{bmatrix}},$ where a_(k) (k=1,2, . . . m) range over the set of complex numbers, where m is the number of an antenna element in the array.
 14. The method of claim 10, wherein the covariance matrix C is generated according to the following equation: $C = {\sum\limits_{j = 1}^{J}{I_{j}\quad{I_{j}^{H}.}}}$
 15. The method of claim 10, wherein the fictitious array manifold A_(f) is used to form the space-time manifold and the space-time manifold operates to resolve the multi-path delays
 16. The method of claim 10, wherein the step of resolving the covariance matrix C to determine multi-path delays τ_(i) uses multiple signal classification techniques.
 17. The method of claim 10, wherein the step of resolving the covariance matrix C to determine multi-path delays τ_(i) uses Alternating Projection.
 18. A system for estimating the multi-path delays τ_(i) in a signal using a spatially blind antenna array comprising: an antenna array for receiving the signal; a means for generating an impulse response h_(k) for each antenna k in the antenna array; a means determining a vectorized space-time impulse response I over the antenna array; a means for creating a covariance matrix C a means for creating a fictitious manifold A_(f), wherein A_(f) is spatially blind and independent of the array characteristics; and, a means for resolving the covariance matrix C with the fictitious manifold A_(f) to estimate the multi-path delays τ_(i) independent of the array characteristics.
 19. The system of claim 18, wherein the fictitious array manifold A_(f) in part forms the space-time manifold and a space-time manifold operates to resolve the multi-path delays 